Basic Linear Algebra 2nd Edition

Basic Linear Algebra Is A Text For First Year Students Leading From Concrete Examples To Abstract Theorems, Via Tutorial-type Exercises. More Exercises (of The Kind A Student May Expect In Examination Papers) Are Grouped At The End Of Each Section. The Book Covers The Most Important Basics Of Any First Course On Linear Algebra, Explaining The Algebra Of Matrices With Applications To Analytic Geometry, Systems Of Linear Equations, Difference Equations And Complex Numbers. Linear Equations Are Treated Via Hermite Normal Forms Which Provides A Successful And Concrete Explanation Of The Notion Of Linear Independence. Another Important Highlight Is The Connection Between Linear Mappings And Matrices Leading To The Change Of Basis Theorem Which Opens The Door To The Notion Of Similarity. This New And Revised Edition Features Additional Exercises And Coverage Of Cramer's Rule (omitted From The First Edition). However, It Is The New, Extra Chapter On Computer Assistance That Will Be Of Particular Interest To Readers: This Will Take The Form Of A Tutorial On The Use Of The Linearalgebra Package In Maple 7 And Will Deal With All The Aspects Of Linear Algebra Developed Within The Book. 1. The Algebra Of Matrices -- 2. Some Applications Of Matrices -- 3. Systems Of Linear Equations -- 4. Invertible Matrices -- 5. Vector Spaces -- 6. Linear Mappings -- 7. The Matrix Connection -- 8. Determinants -- 9. Eigenvalues And Eigenvectors -- 10. The Minimum Polynomial -- 11. Computer Assistance -- 12. Solutions To The Exercises. By T. S. Blyth, E. F. Robertson. Basic Linear Algebra is a text for first year students, working from concrete examples towards abstract theorems, via tutorial-type exercises. The book explains the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations, and complex numbers. Linear equations are treated via Hermite normal forms, which provides a successful and concrete explanation of the notion of linear independence. Another highlight is the connection between linear mappings and matrices, leading to the change of basis theorem which opens the door to the notion of similarity. The authors are well known algebraists with considerable experience of teaching introductory courses on linear algebra to students at St Andrews. This book is based on one previously published by Chapman and Hall, but it has been extensively updated to include further explanatory text and fully worked solutions to the exercises that all 1st year students should be able to answer. "Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers." "Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity."--Jacket